Mellin Analysis, Transform Theory, and Applications A Self-Contained Approach /
This monograph presents the theory of the Mellin transform and the resulting Mellin analysis in a rigorous and unified manner. Often dismissed as a subordinate topic within Fourier and Laplace transform, it is instead demonstrated here that the theory is completely independent, can be studied within...
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| Kieli: | englanti |
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Springer Nature Switzerland : Imprint: Birkhäuser,
2025.
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| Painos: | 1st ed. 2025. |
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| Linkit: | https://doi.org/10.1007/978-3-031-96672-9 |
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| 100 | 1 | |a Bardaro, Carlo. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Mellin Analysis, Transform Theory, and Applications |h [electronic resource] : |b A Self-Contained Approach / |c by Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini, Gerhard Schmeisser. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Birkhäuser, |c 2025. | |
| 300 | |a 1 online resource (XXI, 483 p. 1 illus.). |b 1 illus. in color. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 341 | 0 | |b PDF/UA-1 |2 onix | |
| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
| 341 | 0 | |b Use of color is not sole means of conveying information |2 onix | |
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| 505 | 0 | |a - 1. Preliminaries -- 2. Polar-Analytic Functions -- 3. The Foundation of Mellin Analysis -- 4. The Mellin Convolution -- 5. The Finite Mellin transform and the Mellin–Fourier Series -- 6. The Mellin Transform in Xc -- 7. The Mellin Transform in Spaces Xp/c for 1 < p ≤ 2 -- 8. Mellin Bandlimited Functions and Paley–Wiener Theorems in Mellin Setting -- 9. Mellin Transforms and Fractional Analysis -- 10. The Mellin Distance -- 11. Mellin Transform Methods for Partial Differential Equations -- 12. Exponential Sampling Theory -- 13. Generalized Exponential Sampling Theory -- 14. Applications to Quadrature over the Positive Real Axis. | |
| 520 | |a This monograph presents the theory of the Mellin transform and the resulting Mellin analysis in a rigorous and unified manner. Often dismissed as a subordinate topic within Fourier and Laplace transform, it is instead demonstrated here that the theory is completely independent, can be studied within a self-contained framework, and exhibits some typical characteristics. In addition to highlighting the foundations of the theory, the book addresses applications to certain partial differential equations, sampling theory and numerical quadrature. These applications provide methods which are in turn of interest in various areas of mathematics, science, and engineering. Each chapter is enriched by numerous references to further literature and potential research directions. Researchers working in this field will gain new insights and appreciate the deserved attention for this underrated topic in harmonic analysis. | ||
| 532 | 8 | |a Accessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility, including screen reader support, described non-text content (images, graphs), bookmarks for easy navigation, keyboard-friendly links and forms and searchable, selectable text. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. Please note that a more accessible version of this eBook is available as ePub. | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Fourier analysis. | |
| 650 | 0 | |a Functions of complex variables. | |
| 650 | 0 | |a Special functions. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 1 | 4 | |a Fourier Analysis. |
| 650 | 2 | 4 | |a Functions of a Complex Variable. |
| 650 | 2 | 4 | |a Special Functions. |
| 650 | 2 | 4 | |a Functional Analysis. |
| 700 | 1 | |a Butzer, Paul L. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Mantellini, Ilaria. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Schmeisser, Gerhard. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031966712 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031966736 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031966743 |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-96672-9 |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||
| 950 | |a Focus Bundle Mathematics and Statistics (SpringerNature-85421) | ||